The history museum is hosting a special exhibition on history of flight. The admission ticket for each adult costs $3 and the admission ticket for each child costs $2. On the opening day of the exhibition, 60 tickets were sold for a total of $160. How many adults visited the special exhibition?

Answer 1

Let A be the number of adult tickets and C be the number of child tickets sold.

From the given information:
A + C = 60
3A + 2C = 160

Using the first equation, we can express C in terms of A:
C = 60 - A

Substitute the expression for C into the second equation:
3A + 2(60 - A) = 160
3A + 120 - 2A = 160
A + 120 = 160
A = 40

Therefore, 40 adult tickets were sold on the opening day of the exhibition.

Answer 2

A bridge is sketched in the coordinate plane as a parabola represented by the equation h=40-0.01x^2, where h refers to the height, in feet, of the bridge at a location of x feet from the middle of the bridge. The bridge starts and ends at the x-intercepts of the parabola.
What is the length of this bridge?

Do not round your answer until your end result. When finding the length of the bridge round to the nearest tenth of a foot.

Answer 3

The length of the bridge can be determined by finding the distance between the x-intercepts of the parabola.

To find the x-intercepts, we set h (the height) to 0:
0 = 40 - 0.01x^2
0.01x^2 = 40
x^2 = 4000
x = ±√4000
x = ± 63.2

The length of the bridge is the distance between these two x-values:
Length of the bridge = 2 * 63.2 = 126.4 feet

Therefore, the length of the bridge is 126.4 feet.